1)Let A=, where a and b are postive integers.
Prove that A≠2015. (HINT-Use Modular Arithmetic or Try to use the concept of Odd-Even numbers)
2)Prove that any prime number, cannot be represented as a difference of 2 fifth powers of integers.(HINT-Expand the expression and You will get something in common)
3)Find all pairs (x,y) where x and y are integers such that .(HINT-Try to apply identities)
Then Prove that,
5)Prove that is divisible by 7.(HINT-Use Modular Arithmetic or Apply the concept of .)
Today I have posted some easy problems ,So I'm sure that you will be able to solve all these 5 problems in 1.5 hours.
Also try my Set RMO.